How to Find Upper Limit and Lower Limit?

At times in a normal distribution of a statistical data we would find the need of calculating the upper and lower limits. For instance, finding the upper and lower limits for medicines that should be given to the patients is required to be evaluated.

So, let us learn how to find upper limit and lower limit for any distribution as follows:

In graph the upper limit is shown as U and lower limit as L. We convert half of the % to decimal. In our example we would get: 0.25. Next we check the Z – table for value we got as decimal number in the previous step. We write the closest value for the answer. In our example we would get the closest value as: 0.2770 for 0.2500. This score is positive i.e. right hand score on the z – table and is represented as: U in the graph.

Next we substitute this score in the equation:

U = z S.D. + M,

Where, S.D. is the Standard Deviation and M is the Mean of the distribution. Thus we get the corresponding value of the upper limit. We then find the lower limit L by making the sign of z score as negative and using the same formula again.
L = z S.D. + M.1st we find out the various quantities we would need like mean, standard deviation, variance, mid % amount of the distribution. Next we draw the plot for distribution such that mean is placed in the middle. We shade the portion on the either side of mean representing the middle %. For instance, if the mean is 50 lt., and we have been asked to find the upper and lower measures for the middle % as 50 %, we would draw the graph as follows: